Figure 4: The impact of measurement error on discrimination and ordering. Scatterplot comparing the total scores (true score plus measurement error) of the 30 subjects of Figure 3, with their true scores. Three pairs of subjects have been highlighted to illustrate changes in discrimination and ordering due to measurement error.

Mentions:
This example suggests that Ferguson's δ is hardly affected by measurement error. However, if we compare the total scores (true + error) with the true scores (Figure 4), we see that the discrimination between subjects arises from error in many cases. For illustrative purposes, three pairs of subjects in Figure 4 have been highlighted. Subjects A1 and A2, who are truly different, end up in the same score category, so they cannot be discriminated, due to error. On the other hand, subjects B1 and B2, who have the same true score, end up being discriminated from each other, due to error. For subjects C1 and C2 the very ordering of their discrimination has been reversed: C2 scores higher than C1 on the true score, but C1 scores higher on the total score due to measurement error. All these erroneous discriminations do not seem to affect δ at all.

Figure 4: The impact of measurement error on discrimination and ordering. Scatterplot comparing the total scores (true score plus measurement error) of the 30 subjects of Figure 3, with their true scores. Three pairs of subjects have been highlighted to illustrate changes in discrimination and ordering due to measurement error.

Mentions:
This example suggests that Ferguson's δ is hardly affected by measurement error. However, if we compare the total scores (true + error) with the true scores (Figure 4), we see that the discrimination between subjects arises from error in many cases. For illustrative purposes, three pairs of subjects in Figure 4 have been highlighted. Subjects A1 and A2, who are truly different, end up in the same score category, so they cannot be discriminated, due to error. On the other hand, subjects B1 and B2, who have the same true score, end up being discriminated from each other, due to error. For subjects C1 and C2 the very ordering of their discrimination has been reversed: C2 scores higher than C1 on the true score, but C1 scores higher on the total score due to measurement error. All these erroneous discriminations do not seem to affect δ at all.

Bottom Line:
A critique of Hankins, M: 'How discriminating are discriminative instruments?' Health and Quality of Life Outcomes 2008, 6:36.